document.write( "Question 951063: there are two real numbers. taking half of one is the same as adding 12.5 to the other; the square of the two real numbers are 200 apart \n" ); document.write( "
Algebra.Com's Answer #580801 by ankor@dixie-net.com(22740)\"\" \"About 
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there are two real numbers.
\n" ); document.write( "a & b
\n" ); document.write( " taking half of one is the same as adding 12.5 to the other;
\n" ); document.write( ".5a = b + 12.5
\n" ); document.write( "multiply both side by 2
\n" ); document.write( "a = 2(b+12.5)
\n" ); document.write( "a = 2b + 25
\n" ); document.write( "the squares of the two real numbers are 200 apart
\n" ); document.write( " a^2 - b^2 = 200
\n" ); document.write( "replace a with (2b+25)
\n" ); document.write( "(2b+25)^2 - b^2 = 200
\n" ); document.write( "FOIL
\n" ); document.write( "4b^2 + 100b + 625 - b^2 = 200
\n" ); document.write( "4b^2 - b^2 + 100b + 625 - 200 = 0
\n" ); document.write( "3b^2 + 100b + 425 = 0
\n" ); document.write( "You can use the quadratic formula a=3; b=100 c=425, this will factor to:
\n" ); document.write( "(3b + 85)(b + 5) = 0
\n" ); document.write( "3b = -85
\n" ); document.write( "b = -85/3
\n" ); document.write( "b =28.3333
\n" ); document.write( "and
\n" ); document.write( "b = -5, let's stick with the integer
\n" ); document.write( "find a
\n" ); document.write( "a =2(-5) + 25
\n" ); document.write( "a = -10 + 25
\n" ); document.write( "a = +15
\n" ); document.write( ":
\n" ); document.write( "The 2 numbers are 15 and -5
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check in the equation a^2 - b^2 = 200
\n" ); document.write( "15^2 - (-5^2) =
\n" ); document.write( "225 - 25 = 200
\n" ); document.write( " \n" ); document.write( "
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